An ant crawls from one corner of a room to the diagonally : GMAT Problem Solving (PS)
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# An ant crawls from one corner of a room to the diagonally

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Joined: 28 Mar 2012
Posts: 321
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 29

Kudos [?]: 406 [1] , given: 23

An ant crawls from one corner of a room to the diagonally [#permalink]

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13 Jun 2012, 04:48
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Difficulty:

95% (hard)

Question Stats:

24% (01:50) correct 76% (01:08) wrong based on 123 sessions

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An ant crawls from one corner of a room to the diagonally opposite corner along the shortest possible path. If the dimensions of the room are 3 x 3 x 3, what distance does the ant cover?

A. $$3\sqrt{2}+3$$

B. $$6\sqrt{2}$$

C. $$3*3^{\frac 13}$$

D. $$3\sqrt{5}$$

E. $$9$$
[Reveal] Spoiler: OA
Manager
Status: Rising GMAT Star
Joined: 05 Jun 2012
Posts: 133
Location: Philippines
Concentration: General Management, Finance
GMAT 1: 660 Q V
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WE: Corporate Finance (Consulting)
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Kudos [?]: 55 [1] , given: 16

Re: An ant crawls from one corner of a room to the diagonally [#permalink]

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13 Jun 2012, 05:19
1
KUDOS
1
This post was
BOOKMARKED
An ant crawls from one corner of a room to the diagonally opposite corner along the shortest possible path. If the dimensions of the room are 3 x 3 x 3, what distance does the ant cover?

A. $$3\sqrt{2}+3$$

B. $$6\sqrt{2}$$

C. $$3*3^{\frac 13}$$

D. $$3\sqrt{5}$$

E. $$9$$

This is a Physics question LOL

Anyway, for any dimension of a room that has dimensions a, b and c, the length of the shortest path is:

minimum among (1) square root[(a+b)^2 + c^2] (2) square root[(b+c)^2 + a^2] (3) square root](a+c)^2 + b^2\

Since we have dimensions 3, 3 and 3 we can try any of the three:

square root [(3+3)^2 + 3^2]= square root [6^2 + 9] = square root [36 +9] = square root [45] = square root [9*5] = 3 square root 5

Now how about some kudos, yes?
_________________

Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat.
- T. Roosevelt

Joined: 28 Mar 2012
Posts: 321
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 29

Kudos [?]: 406 [0], given: 23

Re: An ant crawls from one corner of a room to the diagonally [#permalink]

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13 Jun 2012, 05:51
gmatsaga wrote:
An ant crawls from one corner of a room to the diagonally opposite corner along the shortest possible path. If the dimensions of the room are 3 x 3 x 3, what distance does the ant cover?

A. $$3\sqrt{2}+3$$

B. $$6\sqrt{2}$$

C. $$3*3^{\frac 13}$$

D. $$3\sqrt{5}$$

E. $$9$$

This is a Physics question LOL

Anyway, for any dimension of a room that has dimensions a, b and c, the length of the shortest path is:

minimum among (1) square root[(a+b)^2 + c^2] (2) square root[(b+c)^2 + a^2] (3) square root](a+c)^2 + b^2\

Since we have dimensions 3, 3 and 3 we can try any of the three:

square root [(3+3)^2 + 3^2]= square root [6^2 + 9] = square root [36 +9] = square root [45] = square root [9*5] = 3 square root 5

Now how about some kudos, yes?

You are good at googling..!
This indeed is a physics problem, but many variants of this problem are asked in various competitive exams.
If one can do this, then similar concept can be extended to squares, rectangles or even cylinders.

Anyways, it is good problem

Regards,
Manager
Status: Rising GMAT Star
Joined: 05 Jun 2012
Posts: 133
Location: Philippines
Concentration: General Management, Finance
GMAT 1: 660 Q V
GPA: 3.22
WE: Corporate Finance (Consulting)
Followers: 7

Kudos [?]: 55 [0], given: 16

Re: An ant crawls from one corner of a room to the diagonally [#permalink]

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13 Jun 2012, 06:08
gmatsaga wrote:
An ant crawls from one corner of a room to the diagonally opposite corner along the shortest possible path. If the dimensions of the room are 3 x 3 x 3, what distance does the ant cover?

A. $$3\sqrt{2}+3$$

B. $$6\sqrt{2}$$

C. $$3*3^{\frac 13}$$

D. $$3\sqrt{5}$$

E. $$9$$

This is a Physics question LOL

Anyway, for any dimension of a room that has dimensions a, b and c, the length of the shortest path is:

minimum among (1) square root[(a+b)^2 + c^2] (2) square root[(b+c)^2 + a^2] (3) square root](a+c)^2 + b^2\

Since we have dimensions 3, 3 and 3 we can try any of the three:

square root [(3+3)^2 + 3^2]= square root [6^2 + 9] = square root [36 +9] = square root [45] = square root [9*5] = 3 square root 5

Now how about some kudos, yes?

You are good at googling..!
This indeed is a physics problem, but many variants of this problem are asked in various competitive exams.
If one can do this, then similar concept can be extended to squares, rectangles or even cylinders.

Anyways, it is good problem

Regards,

Hehe is that a good thing or a bad thing?

Anyway, this is the first time I encountered such type of question. I can only remember the greatest distance (deluxe Pythagorean theorem). If my memory serves me right we could also use Calculus here. Does the topic multi-variable Calculus ring any bell?
_________________

Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat.
- T. Roosevelt

Joined: 28 Mar 2012
Posts: 321
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 29

Kudos [?]: 406 [8] , given: 23

Re: An ant crawls from one corner of a room to the diagonally [#permalink]

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13 Jun 2012, 07:25
8
KUDOS
1
This post was
BOOKMARKED
Quote:
Hehe is that a good thing or a bad thing?

Anyway, this is the first time I encountered such type of question. I can only remember the greatest distance (deluxe Pythagorean theorem). If my memory serves me right we could also use Calculus here. Does the topic multi-variable Calculus ring any bell?

Hi gmatsaga,

The concept of this question is to open up the surfaces and consider two adjacent surfaces as a plane. (Check the diagram below)
Thus, using the classical Pythagoras concept, the hypotenuse (or the shortest distance between two points) would be calculated as:
$$\sqrt{(3+3)^2+3^2} = 3\sqrt{5}$$

well talking about calculus, I would only say out of scope!

Regards,
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Manager
Status: Rising GMAT Star
Joined: 05 Jun 2012
Posts: 133
Location: Philippines
Concentration: General Management, Finance
GMAT 1: 660 Q V
GPA: 3.22
WE: Corporate Finance (Consulting)
Followers: 7

Kudos [?]: 55 [0], given: 16

Re: An ant crawls from one corner of a room to the diagonally [#permalink]

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13 Jun 2012, 16:52
Quote:
Hehe is that a good thing or a bad thing?

Anyway, this is the first time I encountered such type of question. I can only remember the greatest distance (deluxe Pythagorean theorem). If my memory serves me right we could also use Calculus here. Does the topic multi-variable Calculus ring any bell?

Hi gmatsaga,

The concept of this question is to open up the surfaces and consider two adjacent surfaces as a plane. (Check the diagram below)
Thus, using the classical Pythagoras concept, the hypotenuse (or the shortest distance between two points) would be calculated as:
$$\sqrt{(3+3)^2+3^2} = 3\sqrt{5}$$

well talking about calculus, I would only say out of scope!

Regards,

Did I tell you you're good?

AMAZING!!!!!
_________________

Far better is it to dare mighty things, to win glorious triumphs, even though checkered by failure... than to rank with those poor spirits who neither enjoy nor suffer much, because they live in a gray twilight that knows not victory nor defeat.
- T. Roosevelt

Intern
Joined: 03 Jun 2012
Posts: 32
Location: United States
WE: Project Management (Computer Software)
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Kudos [?]: 41 [0], given: 2

Re: An ant crawls from one corner of a room to the diagonally [#permalink]

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13 Jun 2012, 18:15
Thanks for the magical explanation cj ...you deserve some kudos for this!
Joined: 28 Mar 2012
Posts: 321
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 29

Kudos [?]: 406 [1] , given: 23

Re: An ant crawls from one corner of a room to the diagonally [#permalink]

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13 Jun 2012, 23:07
1
KUDOS
gmatdog wrote:
Thanks for the magical explanation cj ...you deserve some kudos for this!

gmatsaga wrote:
Did I tell you you're good?
AMAZING!!!!!

Thanks

I appreciate the appreciation.
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Re: An ant crawls from one corner of a room to the diagonally [#permalink]

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19 Jan 2014, 04:19
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Re: An ant crawls from one corner of a room to the diagonally [#permalink]

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03 May 2015, 17:47
Hello from the GMAT Club BumpBot!

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Re: An ant crawls from one corner of a room to the diagonally [#permalink]

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05 Nov 2016, 00:16
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: An ant crawls from one corner of a room to the diagonally   [#permalink] 05 Nov 2016, 00:16
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